LINEARIZABILITY OF NONLINEAR FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS BY A GENERALIZED SUNDMAN TRANSFORMATION
We present the linearization problem of fourth-order ordinary differential equation under the generalized Sundman transformation We found the necessary and sufficient conditions which allow the fourth-order ordinary differential equation to be transformed to The process of getting the linearizing transformation is constructed symmetrically and explicitly. Some examples of linearizable equation are provided to demonstrate our procedure and also the linearization of traveling waves of partial differential equation is applied.
linearization problem, generalized Sundman transformation, nonlinear ordinary differential equations.